Difference between Gabor filtering and Discrete Wavelet Transform

Question

Both Gabor filtering and discrete wavelet transform (DWT) analyze the image in both spatial and frequency domains, unlike Fourier transform which analyzes the image only in the frequency domain. What is the difference between DWT and Gabor filtering?

Answer 1

Per se, a Gabor filter in image processing is one linear filter at a certain scale and 2D frequency used for orientation filtering and texture analysis.

It would be easier to compare Gabor representations and discrete wavelet transforms. Both are related to a linear decomposition of possibility multidimensional data at different scales with somehow oscillating functions. Main differences are:

• Discrete wavelets: critical or non-redundant scheme (stable, invertible), discretize some families of wavelets, more scale-based though wavelets range from weakly oscillating (Haar) to oscillation (Shannon), often applied separably across dimensions so weakly directional, a lot of statistical and approximation properties (moments, regularity). Their redundant counterparts: discretized continuous wavelets, shift-invariant or stationary wavelets.

• Gabor transforms: (highly) redundant decomposition, mostly one shape: a modulated Gaussian, more frequency-based though computed at a couple of scale (Gaussian spread), inherently non-separable or directional. Their non-redundant counterparts: modulated or orthogonal lapped transforms, Malvar wavelets.